1. Lecture 19: Real Gases and Condensation
Improvement of Ideal Gas Law: Van der Waals Equation of State
Critical Point: The Onset of Condensation
Intermolecular Forces

2. Collision Rate and Mean Free Path
Imagine following a particular molecule moving through a gas for one second:
hit
miss d
crel x 1s = c (m)
How many collisions will our molecule make per second?

3. PRS Question:
Air has a density of about 1 g/L at room temperature and pressure
Solid nitrogen has a density of about 1 g/cm3
Estimate the volume of one nitrogen molecule for the purpose of estimating the collision rate in air.
L/mol
mol/cm3
cm3/mol
L/mol
28 mol/cm3
28 cm3/mol

4. d ~ [(28 cm3/mol)/(6x1023/mol)]1/3 = 3.6x10-8 cm = 3.6x10-10 m
l = (V/n)/(pd2) = [(28 L/mol)(10-3 m3/L)/(6x1023/mol)]/[3.14 x (3.6x10-10 m)2]
= 1.1x10-7 m = 110 nm
At 500 m/s, there are about 2x10-5 s between collisions.
What is good about this as an estimate?
What is bad about it?

5. Attenuation data for the scattering of a thermal beam (1100 K) of CsCl by Ar atoms and by the polar CH2F2 molecules in a 44 mm cell. The log of the transmission decreases linearly with the pressure of the target gas. [Adapted from H. Schumacher, R. B. Bernstein, and E.W. Rothe, J. Chem. Phys. 33, 584 (1960).]

6. The Ideal Gas Law is Remarkably Good at High T
When does it break down?

8. In which is the mean free path of molecular motion largest?
liquid water at 1 atm and 298K
CO2 at its critical point
CO2 at 1atm pressure and 298K
CO2 at 1 atm pressure and 596K

9. Predict which a cation of sodium is most strongly attracted to:
Br- anion
HBr molecule
Kr atom
H2O molecule